|I guess PS/2 means a wired keyboard.|
It has to be a PS/2 keyboard because the software that drives the keyboard is built into the BIOS chip and is operational as soon as power is applied.
You probably couldn't even do what you describe with a USB keyboard which is also wired as the software for that has to be first loaded by the BIOS and to do that the computer has to be running.
It should be remembered that with the ATX power supply there is always a small amount of current being supplied to the motherboard as long as power is available although everything appears to be turned off and lifeless.
This is to allow things like Wake on Lan, Wake on Ring and to work. Even the On/Off button at the front of the computer needs some software support from the BIOS to work.